SOLVING NONCONVEX NONLINEAR-PROGRAMMING AND MIXED-INTEGER NONLINEAR-PROGRAMMING PROBLEMS WITH ADAPTIVE RANDOM SEARCH

An adaptive random-search optimization algorithm is presented, which is found to be efficient in dealing with nonconvex nonlinear programming (NLP) problems and mixed-integer nonlinear programming (MINLP) problems. The algorithm is an extension of a previously reported algorithm which successfully solved for the global optimum of difficult multimodal unconstrained and constrained NLP problems. The proposed algorithm treats integer variables as discrete integer variables thus avoiding approximations which could produce either infeasible results or a wrong solution to the optimization problem. The algorithm does not require any problem decomposition, neither identification or elimination of nonconvexities, prior to its application. It was tested with several nonconvex NLP and MINLP problems published in the literature, and the results obtained reveal its adequacy for the optimization of nonconvex NLP and small to medium scale MINLP problems encountered in chemical engineering practice. A simple two-phase relaxation strategy is proposed which overcomes some of the difficulties associated with the solution of ill-conditioned or larger scale MINLP problems.